报告题目：Negligibility of Haptotaxis Effect in a Chemotaxis-haptotaxis Model
报 告 人：向田副教授 中国人民大学
时间：2021年9月30日（周五）10:00 --11:00
腾讯会议：https://meeting.tencent.com/dm/WmFlzGodRn7b
会 议 ID：474 320 007
Abstract：
In this talk, we rigorously study chemotaxis effect versus haptotaxis effect on boundedness, blow-up and asymptotical behavior of solutions for a chemotaxis-haptotaxis model in 2D settings (3D setting will also be mentioned if time permits). It is well-known that the corresponding Keller-Segel chemotaxis-onlymodelpossessesa striking feature of critical mass blowup phenomenon, namely, subcritical massensures boundedness, whereas, supercritical mass induces the existence of blow-ups. Herein, we show that this critical mass blow-up phenomenon stays almost the same in the full chemotaxis-haptotaxis model and that any global-in-time haptotaxis solution component vanishes exponentially and the other two solution components converge exponentially to that of chemotaxis-only model in a global sense for suitably large chemo-sensitivity and in the usual sense for suitably small chemo-sensitivity. Therefore, haptotaixs is neither good nor bad than chemotaxis, showing negligibility of haptotaxis effect in the underlying chemotaxis-haptotaxis model.
讲座预告
2021年9月30日精密测量院数学及应用研究部2021年学术报告（二十三）
报告题目：Negligibility of Haptotaxis Effect in a Chemotaxis-haptotaxis Model报 告 人：向田 副教授 中国人民大学
时 间：2021年9月30日（周五）10:00 --11:00
腾讯会议：https://meeting.tencent.com/dm/WmFlzGodRn7b
会 议 ID：474 320 007
Abstract：
In this talk, we rigorously study chemotaxis effect versus haptotaxis effect on boundedness, blow-up and asymptotical behavior of solutions for a chemotaxis-haptotaxis model in 2D settings (3D setting will also be mentioned if time permits). It is well-known that the corresponding Keller-Segel chemotaxis-only model possesses a striking feature of critical mass blowup phenomenon, namely, subcritical mass ensures boundedness, whereas, supercritical mass induces the existence of blow-ups. Herein, we show that this critical mass blow-up phenomenon stays almost the same in the full chemotaxis-haptotaxis model and that any global-in-time haptotaxis solution component vanishes exponentially and the other two solution components converge exponentially to that of chemotaxis-only model in a global sense for suitably large chemo-sensitivity and in the usual sense for suitably small chemo-sensitivity. Therefore, haptotaixs is neither good nor bad than chemotaxis, showing negligibility of haptotaxis effect in the underlying chemotaxis-haptotaxis model.
个人简介：
向田，2014年5月博士毕业于美国杜兰大学（Tulane University），偏微分方程专业，现为人民大学数学科学研究院副教授，博士生导师。研究兴趣为偏微分方程及其应用, 已在MMMAS, CVPDE, SIAP, JDE, Nonlinearity, JNS等杂志上发表三十篇论文，被引用300余次(mathscinet)，研究获得中央高校科研启动基金，人民大学人才培育基金，博士后基金一等，国家自然科学基金青年以及面上基金的资助。